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In summary, K refers to the surface current density, which is defined as the current per unit width-perpendicular-to-flow. It is related to the mobile surface charge density and velocity. The integral form of K can be written as I_surface = ∫K·dl, where ∫ is a path across the surface. In the statement mentioned, A is also in the x direction due to the direction of K. Permeable refers to the material being linear with respect to some constant called "miu".
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Palindrom
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K, the "idealized surface current density"
Hey, I don't quite understand that guy, K.
I have an exam on Sunday in E&M, I'm studying from Jackson. I haven't found any definition of 'K'.
If anyone could give me a rigurous definition and an integral form, if there's any, I'd appreciate it.
Oh, and since we're at it, I stumped into that next statement:
"Suppose that the upper half of space is filled with a permeable media, while the other half is empty space. If, in the x-y plane, K is in the x direction, it follows that A (vector potential) is also in that direction in the entire space".
Huh?
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quasar987
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What definition do you have so far with which you are unsatisfied?
Griffiths (pp.211) gives the following definition: "When charge flows over a surface, we describe it by the surface current density K, defined as follows: Consider a "ribbon" of infinitesimal width [itex]dl_\perp[/itex], running parallel to the flow. If the current in this ribbon is [itex]d\vec{I}[/itex], the surface current density is
[tex]\vec{K}=\frac{d\vec{I}}{dl_\perp}[/tex]
In words, K is the current per unit width-perpendicular -to-flow. In particular, if the (mobile) surface charge density is [itex]\sigma[/itex] and the velocity is [itex]\vec{v}[/itex], then
[tex]\vec{K}=\sigma \vec{v}[/tex]"
It is not written but I believe we can write the integral form as
[tex]I_{surface} = \int_{\mathcal{P}}\vec{K}\cdot d\vec{l}[/tex]
where [itex]\mathcal{P}[/itex] is a path across the surface.
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Palindrom
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Thanks.
But then, in the statement I gave, why is A in the x direction? I just can't see it.
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quasar987
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I don't know what permeable means, I'll have to leave that one to someone else.
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Palindrom
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It may not be the right term. It simply means it's a linear matter for some 'miu'.
FAQ: K, the idealized surface current density
What is the concept of "K, the idealized surface current density"?
K, the idealized surface current density, is a theoretical concept used in electromagnetism to describe the flow of electric current on a surface. It is represented by the symbol K and is typically measured in amperes per meter squared.
How is "K" related to other electrical properties?
K is closely related to other electrical properties such as electric field and electric potential. It is defined as the product of the electric field and the electrical conductivity of the material. This means that higher values of K indicate a stronger flow of current on the surface.
What are the units of "K"?
The units of K, the idealized surface current density, are amperes per meter squared. This can also be written as A/m² or A·m⁻².
What factors can affect the value of "K"?
The value of K can be affected by several factors, including the properties of the material (such as electrical conductivity and surface roughness), the strength and direction of the electric field, and the presence of any external magnetic fields.
How is "K" used in practical applications?
K, the idealized surface current density, is used in practical applications such as designing electrical circuits and analyzing the behavior of electromagnetic devices. It is also used in the study of electrochemistry and in the development of new materials for electronic devices.
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